Is 12.2882057274 rational or irrational

Answer 1

12.2882057274 is rational, but it is a rational approximation of an irrational number.

Any number that can be expressed exactly as a fraction is rational, and that includes any number that, when written in decimal form, uses a finite number of digits.

However, √151 (the square root of 151), which is approximately 12.2882057274445..., is an irrational number. You could keep getting a closer and closer approximation with more and more digits, but you would never hit it exactly, and you will never end up with a repeating series of digits.

0.80428571428571428571428571... is also a rational number, because, after the 0.80 at the beginning, you have a repeating sequence of 428571. It's a decimal representation of 563/700.